So I installed MySQL connector odbc-5.2.7-osx10.7-x86-32bit which is the most recent 32-bit version I found. When I test this with iODBC Administrator, it seems to work, but I get the error mentioned at the beginning when I try the code in R.

The FAQ of iODBC says the following regarding this type of error:

[iODBC] [Driver Manager]Specified driver could not be loaded

There are a few reasons why this could occur, and thinking through the architecture helps. Your application has loaded libiodbc successfully, and it has found an odbc.ini file (or equivalent through the ODBCINI environment variable), and it has found a DSN within that odbc.ini that matches the name requested in your connection.

However, the driver manager has had problems loading the library specified in the `Driver=' line of that DSN definition. Either it doesn't exist, or its permissions are insufficient to allow your application to load it (it must be readable and executable, and the directories leading down to it must be executable), or maybe the file is not a dynamic library - it could be a static library (a *.a file except on AIX) or is otherwise corrupted. These are all things to check, or you may be best off reinstalling the driver if all the permissions check out.